1MA1 · N2–N3NumberFoundation

The Four Operations

Adding, subtracting, multiplying and dividing are the building blocks of all maths. This lesson covers written methods for big numbers and the order you must do operations in (BIDMAS).

45 min Video by Maths Genie Pearson Edexcel GCSE Maths (1MA1)

The big picture

The four operations are not four unrelated rules. Addition and subtraction are inverses; multiplication and division are inverses. Edexcel uses those relationships to test estimation, checking, missing values and multi-step problem solving as well as written calculation.

Multiplying Whole Numbers and DecimalsWatch the walkthrough, then read the notes below.

Open on YouTube

What you'll learn

Add and subtract using column methods
Multiply with long multiplication
Divide using short and long division
Use BIDMAS to do calculations in the right order

Written methods

For addition and subtraction, line the numbers up by place value and work from the right, carrying or borrowing as needed.

For multiplication, long multiplication multiplies by each digit in turn and adds the results. For division, short division (“bus stop”) works for dividing by a single digit.

Why this works

Every formal method is built from place value. Aligning columns ensures that units combine with units and hundredths combine with hundredths.

Tip — Estimate the answer first (e.g. round to the nearest 10) so you can spot a silly mistake.

BIDMAS — the order of operations

When a calculation mixes operations, do them in this order: $B$ rackets, $I$ ndices, $D$ ivision and $M$ ultiplication, then $A$ ddition and $S$ ubtraction.

Brackets \to Indices \to \times \div \to + -

BIDMAS order of operations.

1Multiplication comes before addition.

4 \times 2 = 8

, then

3 + 8 = 11

Answer

11

Why this works

BIDMAS resolves ambiguity. Multiplication and division have equal priority, as do addition and subtraction, so operations at the same level are completed from left to right.

Negative numbers and inverse checks

When signs are mixed, separate the size of the calculation from its direction. For multiplication and division, equal signs give a positive answer and different signs give a negative answer.

Use the inverse operation to check a result. If $47 im es 36 = 1692$ , then $1692 d i v 36$ must return $47$ .

1Translate the journey into

- 3 + 11 - 6

2Calculate from left to right:

- 3 + 11 = 8

8 - 6 = 2

AnswerFloor

2

Why this works

A number line gives meaning to signed arithmetic: adding moves right and subtracting moves left. The sign is a direction, not decoration.

Tip — Estimate before using a calculator. An estimate will catch a misplaced decimal point even when the keystrokes appear correct.

Think like an examiner

Write enough method to make your reasoning visible. In a multi-mark calculation, a correct method can earn credit after a later arithmetic slip.
Do not apply BIDMAS as six rigid consecutive stages: multiplication and division are one priority level, completed left to right.
Include units and interpret the result when a question is set in context.

Remember these

B I DM AS

Brackets, Indices, Divide/Multiply, Add/Subtract.

Watch out for these

Working left to right and getting

3 + 4 \times 2 = 14

Multiply first:

3 + 8 = 11

Forgetting to line digits up by place value in column methods.

Keep units under units, tens under tens, and the decimal points in line.

Stretch yourself

Insert one pair of brackets into $18 - 6 d i v 3 + 1$ to make the answer $5$ .

Hint — Try changing the quantity that is divided by 3.

Questions students ask

Do I always work from left to right?

Only between operations with the same priority. Complete brackets and powers first, then multiplication/division left to right, then addition/subtraction left to right.

How much working should I show?

Show the operation, substitution and important intermediate values. This makes method marks available even if the final arithmetic goes wrong.

Key takeaways

Use neat column methods and estimate to check.
BIDMAS sets the order: Brackets, Indices, ×÷, +−.
Division and multiplication rank equally — work left to right between them.

Test yourself

Ready to practise The Four Operations? Pick a mode and earn XP & Dobloons.

Next step

Practise this topic

Real past-paper questions on The Four Operations, marked mark-by-mark. How you do feeds straight into your weak-topic list, so your revision keeps targeting what actually needs work.

Practise this topic